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 Folding Square II (Posted on 2012-07-25)
You have a square piece of paper and you do not know its length or width.

What is the minimum number of folds required in order for the paper to only show 1/15 of its original size, 2/15 of it's original size, 3/15 of its original size, ........, 14/15 of its original size.

Note: You do not know where one-third marks or one-fifth marks lie on this piece of paper therefore you must use folds to mark these areas. You are allowed to use folds as guides to make other folds.

 No Solution Yet Submitted by K Sengupta Rating: 4.0000 (1 votes)

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 Equal intercepts (part solution) Comment 1 of 1
Part 1 - creating 15 equal areas
Crease square ABCD along diagonal BD.

A      f4       f3       f2        f1        B

s1

t2

o

t1
q1

D                                                C

Then fold into 4 quarters horizontally.
q1 is the intersection of BD with the lower quarter fold.
Crease along C-q1 to form t1 which is 1/3 from D to A.  Fold A to t1 to form t2.

Fold A to t2 and crease to form s1 on BD.  Crease C-s1 to form f1.  f1 is 1/5 of AB. Fold A to s1 to create f3, A to f3 for f4 and f3 to f1 for f2.

With folds horizontal and vertical folds from each of the t1,t2,f1,f2,f3,&f4 we have 15 rectangles of the same size.

Part 2 - displaying n/15's  in part
14/15 - fold A towards o to form the line f3-t2 (area of one 1/15 rectangle removed)
13/15 - fold A towards o to form the line f1-t2 (area of two 1/15 rectangles removed)

 Posted by brianjn on 2012-07-25 21:58:43

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